TSTP Solution File: SCT165+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:17:53 EDT 2023
% Result : Theorem 27.88s 4.65s
% Output : CNFRefutation 27.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 23 unt; 0 def)
% Number of atoms : 172 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 163 ( 68 ~; 58 |; 14 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-4 aty)
% Number of variables : 179 ( 19 sgn; 119 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [X14,X8,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X8),X14))
<=> hBOOL(hAPP(X14,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f63,axiom,
! [X9,X20] :
( X9 != X20
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X20))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(f93,axiom,
! [X14,X11] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool),X14),c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(f251,axiom,
! [X14,X11] :
( class_Finite__Set_Ofinite(X11)
=> c_Finite__Set_Ofinite(X11,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).
fof(f254,axiom,
! [X13,X14,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool),X14),X13))
=> ( c_Finite__Set_Ofinite(X11,X13)
=> c_Finite__Set_Ofinite(X11,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(f257,axiom,
! [X11] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X11),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X11),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(f258,axiom,
! [X11] :
( class_Finite__Set_Ofinite(X11)
=> c_Finite__Set_Ofinite(X11,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).
fof(f432,axiom,
! [X64,X17,X45,X11] :
( c_Finite__Set_Ofinite(X11,X45)
=> c_Finite__Set_Ofinite(X17,c_Set_Oimage(X11,X17,X64,X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(f469,axiom,
! [X17,X8,X1,X11] : hBOOL(hAPP(hAPP(c_member(X11),hAPP(X1,X8)),c_Set_Oimage(X17,X11,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
fof(f485,axiom,
! [X50] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X50)
<=> ? [X4] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X50))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(f517,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f525,axiom,
! [X80,X11] : hAPP(c_COMBI(X11),X80) = X80,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f575,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f56]) ).
fof(f582,plain,
! [X0,X1] :
( X0 != X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ),
inference(rectify,[],[f63]) ).
fof(f608,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f93]) ).
fof(f764,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(X1)
=> c_Finite__Set_Ofinite(X1,X0) ),
inference(rectify,[],[f251]) ).
fof(f766,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0))
=> ( c_Finite__Set_Ofinite(X2,X0)
=> c_Finite__Set_Ofinite(X2,X1) ) ),
inference(rectify,[],[f254]) ).
fof(f769,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f257]) ).
fof(f770,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f258]) ).
fof(f940,plain,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X3,X2)
=> c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
inference(rectify,[],[f432]) ).
fof(f977,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
inference(rectify,[],[f469]) ).
fof(f993,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) ),
inference(rectify,[],[f485]) ).
fof(f1008,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f525]) ).
fof(f1347,plain,
! [X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f764]) ).
fof(f1350,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0)) ),
inference(ennf_transformation,[],[f766]) ).
fof(f1351,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0)) ),
inference(flattening,[],[f1350]) ).
fof(f1354,plain,
! [X0] :
( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f770]) ).
fof(f1473,plain,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(ennf_transformation,[],[f940]) ).
fof(f1528,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) ),
inference(ennf_transformation,[],[f993]) ).
fof(f1604,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) )
& ( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ) ),
inference(nnf_transformation,[],[f575]) ).
fof(f1605,plain,
! [X0,X1] :
( ( X0 != X1
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
| X0 = X1 ) ),
inference(nnf_transformation,[],[f582]) ).
fof(f1606,plain,
! [X0,X1] :
( ( X0 != X1
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
| X0 = X1 ) ),
inference(flattening,[],[f1605]) ).
fof(f1704,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ) ),
inference(nnf_transformation,[],[f769]) ).
fof(f1793,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1528]) ).
fof(f1794,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f1793]) ).
fof(f1795,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK41(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK41(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1796,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK42(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1797,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK41(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK41(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK42(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f1794,f1796,f1795]) ).
fof(f1934,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1604]) ).
fof(f1935,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1604]) ).
fof(f1949,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f1998,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f608]) ).
fof(f2237,plain,
! [X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f1347]) ).
fof(f2240,plain,
! [X2,X0,X1] :
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X2,X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),X0)) ),
inference(cnf_transformation,[],[f1351]) ).
fof(f2246,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1704]) ).
fof(f2247,plain,
! [X0] :
( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2467,plain,
! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(cnf_transformation,[],[f1473]) ).
fof(f2516,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f977]) ).
fof(f2535,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK42(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f1797]) ).
fof(f2574,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f517]) ).
fof(f2582,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f1008]) ).
fof(f2621,plain,
! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_resolution,[],[f1949]) ).
cnf(c_160,plain,
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
inference(cnf_transformation,[],[f1935]) ).
cnf(c_161,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f1934]) ).
cnf(c_172,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f2621]) ).
cnf(c_218,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f1998]) ).
cnf(c_440,plain,
( ~ class_Finite__Set_Ofinite(X0)
| c_Finite__Set_Ofinite(X0,X1) ),
inference(cnf_transformation,[],[f2237]) ).
cnf(c_443,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1),X2))
| ~ c_Finite__Set_Ofinite(X0,X2)
| c_Finite__Set_Ofinite(X0,X1) ),
inference(cnf_transformation,[],[f2240]) ).
cnf(c_448,plain,
( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f2246]) ).
cnf(c_450,plain,
( ~ class_Finite__Set_Ofinite(X0)
| c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f2247]) ).
cnf(c_667,plain,
( ~ c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ofinite(X2,c_Set_Oimage(X0,X2,X3,X1)) ),
inference(cnf_transformation,[],[f2467]) ).
cnf(c_715,plain,
hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,X2)),c_Set_Oimage(X3,X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f2516]) ).
cnf(c_736,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X0),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),sK42(X1))) ),
inference(cnf_transformation,[],[f2535]) ).
cnf(c_773,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f2574]) ).
cnf(c_781,plain,
hAPP(c_COMBI(X0),X1) = X1,
inference(cnf_transformation,[],[f2582]) ).
cnf(c_38307,plain,
hBOOL(hAPP(c_Set_Oimage(X0,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),hAPP(X2,X3))),
inference(superposition,[status(thm)],[c_715,c_161]) ).
cnf(c_46000,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK42(X0)),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(superposition,[status(thm)],[c_736,c_172]) ).
cnf(c_49500,plain,
hBOOL(hAPP(c_Set_Oimage(X0,X1,c_COMBI(X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),X3)),
inference(superposition,[status(thm)],[c_781,c_38307]) ).
cnf(c_53124,plain,
( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X0,X1) ),
inference(superposition,[status(thm)],[c_218,c_443]) ).
cnf(c_53943,plain,
( ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X0),X1) ),
inference(superposition,[status(thm)],[c_448,c_53124]) ).
cnf(c_54209,plain,
( ~ hBOOL(hAPP(X0,sK42(X0)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(superposition,[status(thm)],[c_160,c_46000]) ).
cnf(c_55026,plain,
( ~ class_Finite__Set_Ofinite(X0)
| c_Finite__Set_Ofinite(tc_Option_Ooption(X0),X1) ),
inference(superposition,[status(thm)],[c_440,c_53943]) ).
cnf(c_55299,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X0,X1,c_COMBI(X2),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(superposition,[status(thm)],[c_49500,c_54209]) ).
cnf(c_55413,plain,
( ~ class_Finite__Set_Ofinite(X0)
| c_Finite__Set_Ofinite(tc_Option_Ooption(tc_Option_Ooption(X0)),X1) ),
inference(superposition,[status(thm)],[c_55026,c_53943]) ).
cnf(c_55758,plain,
~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(superposition,[status(thm)],[c_667,c_55299]) ).
cnf(c_56849,plain,
~ class_Finite__Set_Ofinite(X0),
inference(global_subsumption_just,[status(thm)],[c_55413,c_450,c_55758]) ).
cnf(c_56851,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_773,c_56849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.17 % Command : run_iprover %s %d THM
% 0.14/0.37 % Computer : n003.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 24 15:08:53 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.19/0.45 Running first-order theorem proving
% 0.19/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.88/4.65 % SZS status Started for theBenchmark.p
% 27.88/4.65 % SZS status Theorem for theBenchmark.p
% 27.88/4.65
% 27.88/4.65 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 27.88/4.65
% 27.88/4.65 ------ iProver source info
% 27.88/4.65
% 27.88/4.65 git: date: 2023-05-31 18:12:56 +0000
% 27.88/4.65 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 27.88/4.65 git: non_committed_changes: false
% 27.88/4.65 git: last_make_outside_of_git: false
% 27.88/4.65
% 27.88/4.65 ------ Parsing...
% 27.88/4.65 ------ Clausification by vclausify_rel & Parsing by iProver...
% 27.88/4.65
% 27.88/4.65 ------ Preprocessing... sup_sim: 24 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 24 sf_s rm: 21 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 21 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 21 0s sf_e pe_s pe_e
% 27.88/4.65
% 27.88/4.65 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 27.88/4.65
% 27.88/4.65 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.88/4.65 ------ Proving...
% 27.88/4.65 ------ Problem Properties
% 27.88/4.65
% 27.88/4.65
% 27.88/4.65 clauses 435
% 27.88/4.65 conjectures 0
% 27.88/4.65 EPR 19
% 27.88/4.65 Horn 332
% 27.88/4.65 unary 111
% 27.88/4.65 binary 151
% 27.88/4.65 lits 1109
% 27.88/4.65 lits eq 245
% 27.88/4.65 fd_pure 0
% 27.88/4.65 fd_pseudo 0
% 27.88/4.65 fd_cond 11
% 27.88/4.65 fd_pseudo_cond 72
% 27.88/4.65 AC symbols 0
% 27.88/4.65
% 27.88/4.65 ------ Schedule dynamic 5 is on
% 27.88/4.65
% 27.88/4.65 ------ no conjectures: strip conj schedule
% 27.88/4.65
% 27.88/4.65 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 27.88/4.65
% 27.88/4.65
% 27.88/4.65 ------
% 27.88/4.65 Current options:
% 27.88/4.65 ------
% 27.88/4.65
% 27.88/4.65
% 27.88/4.65
% 27.88/4.65
% 27.88/4.65 ------ Proving...
% 27.88/4.65
% 27.88/4.65
% 27.88/4.65 % SZS status Theorem for theBenchmark.p
% 27.88/4.65
% 27.88/4.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.88/4.65
% 27.88/4.65
%------------------------------------------------------------------------------